The Impact of Aging, Dementia, and SES on Cognitive Decline

A Longitudinal Study Using Linear Mixed Models

Adasia M., Bess T., Preethi R.

Introduction

Linear Mixed Models (LMMs) are powerful statistical tools designed to analyze data with complex structures, such as hierarchical data (e.g., individuals within groups) or repeated measures (e.g., assessments taken over time). Unlike traditional methods, LMMs account for variations at both the group level and the individual level, making them ideal for studying patterns of cognitive decline across aging populations.

Why LMMs?

Fixed Effects: Capture overall population trends, like how age or socioeconomic status influences cognitive function on average.
Random Effects: Model differences between individuals, accounting for unique trajectories over time or variability across participants.
Data Flexibility: Handle missing data and unbalanced datasets effectively, ensuring reliable results even when some observations are incomplete.

Literature Review

Linear Mixed Models: An Overview

Extend simple linear regression by incorporating fixed effects (population-level) and random effects (subject-level variability).
Ideal for analyzing longitudinal and hierarchical datasets.
Provide unbiased estimates even with missing data (Bates, 2014; Gelman & Hill, 2007).

Covariance Structure

Essential for modeling dependencies between repeated measures (Starkweather, 2010).
Positive covariance: variables move together.
Negative covariance: variables move in opposite directions.
Allows explicit modeling of within-subject variability, critical for longitudinal studies.

Literature Review Continued

Robust Estimation

Methods that minimize the influence of outliers, ensuring parameter reliability (Agostinelli & Yohai, 2016).
Non-robust techniques like OLS regression are highly sensitive to extreme values and may yield biased results.

Challenges of Traditional Methods

Traditional linear models assume independence of observations, often violated in clustered data (Barr et al., 2013).
Handling missing data through listwise deletion or imputation can introduce bias (Enders, 2010).

Methods

Our Focus

This project applies LMMs to investigate:

The influence of age, dementia status, and socioeconomic factors on cognitive decline.
Cognitive function measured using the Mini-Mental State Examination (MMSE), a widely-used tool for assessing cognitive impairment.
How repeated assessments over time help us understand individual changes in cognitive function while capturing broader population trends.

Methods

Dataset: OASIS-Longitudinal MRI Data in Nondemented and Demented Older Adults

Source: NCBI

Summary of the chosen dataset:

Includes MRI scans of 150 subjects aged 60-96.
Longitudinal data collected over 373 sessions.
Subjects scanned at least twice, with visits separated by at least a year.
Clinical Dementia Rating (CDR) categorized as nondemented or with mild Alzheimer’s disease.
72 were nondemented throughout, while 64 were demented initially and remained so.
Participants were right-handed, consisting of 62 men and 88 women.
Each session had 3-4 T1-weighted MRI scans.

Methods

Modeling Approach

Outcome Variable: Mini-Mental State Exam (MMSE) score.
Fixed Effects: Age, dementia status, SES, and interactions.
Random Effects: Subject ID to capture individual variability.
Software: R (packages: lme4, tableone for data summaries).

R script for Table One

#install.packages("tableone")
library(tableone)

#install.packages("readr")
library(readr)

oasis_longitudinal <- read_csv("C:/IDC6940/IDC6940_BDP/oasis_longitudinal.csv")

# Load necessary library
library(tableone)

# Recode M/F for easier handling in Table 1 (optional)
oasis_longitudinal$Gender <- ifelse(oasis_longitudinal$'M/F' == "M", "Male", "Female")

# Define the variables to be included in Table 1
vars <- c("Age", "Gender", "Hand", "EDUC", "SES", "MMSE", "CDR", "eTIV", "nWBV", "ASF")

# Define the stratifying variable (Group)
strata <- "Group"

# Create Table One
table1 <- CreateTableOne(vars = vars, strata = strata, data = oasis_longitudinal, factorVars = c("Gender", "Hand", "CDR"))

# Print the table with p-values
print(table1, showAllLevels = TRUE, smd = TRUE)

                  Stratified by Group
                   level  Converted        Demented         Nondemented     
  n                            37              146              190         
  Age (mean (SD))           79.76 (7.43)     76.26 (6.94)     77.06 (8.10)  
  Gender (%)       Female      24 ( 64.9)       60 ( 41.1)      129 ( 67.9) 
                   Male        13 ( 35.1)       86 ( 58.9)       61 ( 32.1) 
  Hand (%)         R           37 (100.0)      146 (100.0)      190 (100.0) 
  EDUC (mean (SD))          15.46 (2.52)     13.67 (2.90)     15.14 (2.74)  
  SES (mean (SD))            1.73 (0.96)      2.77 (1.20)      2.39 (1.05)  
  MMSE (mean (SD))          28.68 (1.56)     24.51 (4.50)     29.23 (0.88)  
  CDR (%)          0           18 ( 48.6)        0 (  0.0)      188 ( 98.9) 
                   0.5         19 ( 51.4)      102 ( 69.9)        2 (  1.1) 
                   1            0 (  0.0)       41 ( 28.1)        0 (  0.0) 
                   2            0 (  0.0)        3 (  2.1)        0 (  0.0) 
  eTIV (mean (SD))        1459.27 (135.43) 1485.85 (173.77) 1495.50 (184.89)
  nWBV (mean (SD))           0.72 (0.04)      0.72 (0.03)      0.74 (0.04)  
  ASF (mean (SD))            1.21 (0.11)      1.20 (0.14)      1.19 (0.14)  
                  Stratified by Group
                   p      test SMD   
  n                                  
  Age (mean (SD))   0.045       0.313
  Gender (%)       <0.001       0.371
                                     
  Hand (%)             NA      <0.001
  EDUC (mean (SD)) <0.001       0.433
  SES (mean (SD))  <0.001       0.652
  MMSE (mean (SD)) <0.001       1.041
  CDR (%)          <0.001       5.599
                                     
                                     
                                     
  eTIV (mean (SD))  0.510       0.149
  nWBV (mean (SD)) <0.001       0.465
  ASF (mean (SD))   0.683       0.111

Table One

	level	Converted	Demented	Nondemented	p
n		37	146	190
Female	F	24 ( 64.9)	60 ( 41.1)	129 ( 67.9)	<0.001
Male	M	13 ( 35.1)	86 ( 58.9)	61 ( 32.1)
Dom Hand	R	37 (100.0)	146 (100.0)	190 (100.0)	NA
CDR	0	18 ( 48.6)	0 ( 0.0)	188 ( 98.9)	<0.001
	0.5	19 ( 51.4)	102 ( 69.9)	2 ( 1.1)
	1	0 ( 0.0)	41 ( 28.1)	0 ( 0.0)
	2	0 ( 0.0)	3 ( 2.1)	0 ( 0.0)
Age		79.76 (7.43)	76.26 (6.94)	77.06 (8.10)	0.045
Education		15.46 (2.52)	13.67 (2.90)	15.14 (2.74)	<0.001
SES		1.73 (0.96)	2.77 (1.20)	2.39 (1.05)	<0.001
MMSE		28.68 (1.56)	24.51 (4.50)	29.23 (0.88)	<0.001
eTIV		1459.27 (135.43)	1485.85 (173.77)	1495.50 (184.89)	0.51
nWBV		0.72 (0.04)	0.72 (0.03)	0.74 (0.04)	<0.001
ASF		1.21 (0.11)	1.20 (0.14)	1.19 (0.14)	0.683

Data Visualizations

Age of Participants

Data Visualizations

Gender of Participants

Data Visualizations

Socioeconomic Status of Participants

Data Visualizations

Normalized Whole Brain Volume vs Age

Age as a Predictor of Cognitive Decline

By: Adasia McClinton

Data Cleaning and Ingestion

data <- read.csv("C:/IDC6940/IDC6940_BDP/oasis_longitudinal.csv")
library(mice)
imputed_data <- mice(data, m = 5, method = 'pmm')


 iter imp variable
  1   1  SES  MMSE
  1   2  SES  MMSE
  1   3  SES  MMSE
  1   4  SES  MMSE
  1   5  SES  MMSE
  2   1  SES  MMSE
  2   2  SES  MMSE
  2   3  SES  MMSE
  2   4  SES  MMSE
  2   5  SES  MMSE
  3   1  SES  MMSE
  3   2  SES  MMSE
  3   3  SES  MMSE
  3   4  SES  MMSE
  3   5  SES  MMSE
  4   1  SES  MMSE
  4   2  SES  MMSE
  4   3  SES  MMSE
  4   4  SES  MMSE
  4   5  SES  MMSE
  5   1  SES  MMSE
  5   2  SES  MMSE
  5   3  SES  MMSE
  5   4  SES  MMSE
  5   5  SES  MMSE

imputed_list <- lapply(1:5, function(i) complete(imputed_data, i))

Model 0: Age as the Sole Predictor

Assess whether age alone is a significant predictor of cognitive decline as measured by MMSE scores.

\text{MMSE}_{ij} = 29.660 - 0.031 \times \text{Age}_{ij} + u_{0j} + \epsilon_{ij}

Intercept: 29.660 (baseline MMSE score).
Age Coefficient: -0.031 (small, non-significant decline with age).

Key Findings

Age alone is not a significant predictor of MMSE scores.
Indicates additional variables may explain cognitive decline.

Model 0: Age as the Sole Predictor

R Code

# Model 0: Age as the sole predictor
library("lme4")
library("mitml")
library("Matrix")
model0 <- lapply(imputed_list, function(data) lmer(MMSE ~ Age + (1 | Subject.ID), data = data))
pooled_results <- testEstimates(model0, method = "D2")
summary(pooled_results)


Call:

testEstimates(model = model0, method = "D2")

Final parameter estimates and inferences obtained from 5 imputed data sets.

             Estimate Std.Error   t.value        df   P(>|t|)       RIV       FMI 
(Intercept)    29.718     2.454    12.112 48917.049     0.000     0.009     0.009 
Age            -0.033     0.032    -1.034 39962.092     0.301     0.010     0.010 

Unadjusted hypothesis test as appropriate in larger samples.

Results: The age effect on MMSE was small and non-significant, suggesting that age alone does not fully explain cognitive decline.

Model 1: Adding Dementia Severity and SES

Examine the combined effect of age, dementia severity (CDR), and SES

\text{MMSE}_{ij} = 34.544 - 0.070 \times \text{Age}_{ij} - 4.699 \times \text{GD}_{ij} - 0.231 \times \text{SES}_{ij} + 0.008 \times (\text{Age} \times \text{GD})_{ij} + u_{0j} + \epsilon_{ij}

Age Coefficient: -0.070 (non-significant decline).
CDR Coefficient: -4.699 (significant decline in MMSE).
SES Coefficient: -0.231 (small decline).

Key Findings

Dementia severity significantly predicts MMSE scores.
Age and SES are not significant predictors in this model.

Model 1: Adding Dementia Severity and SES

R Code

model1 <- lapply(imputed_list, function(data) {
  lmer(MMSE ~ Age * Group + SES + (1 | Subject.ID), data = data)
})
pooled_results <- testEstimates(model1, method = "D2")
summary(pooled_results)


Call:

testEstimates(model = model1, method = "D2")

Final parameter estimates and inferences obtained from 5 imputed data sets.

                      Estimate Std.Error   t.value        df   P(>|t|)       RIV       FMI 
(Intercept)             34.551     6.459     5.349 2.606e+05     0.000     0.004     0.004 
Age                     -0.069     0.081    -0.855 2.834e+06     0.392     0.001     0.001 
GroupDemented           -4.465     7.265    -0.615 5.642e+05     0.539     0.003     0.003 
GroupNondemented        -4.165     6.933    -0.601 8.978e+06     0.548     0.001     0.001 
SES                     -0.272     0.216    -1.260 6.970e+01     0.212     0.315     0.260 
Age:GroupDemented        0.007     0.092     0.078 2.177e+05     0.938     0.004     0.004 
Age:GroupNondemented     0.062     0.087     0.708 3.153e+06     0.479     0.001     0.001 

Unadjusted hypothesis test as appropriate in larger samples.

Results: This model showed no significant effects for age, SES, or age-by-group interactions, indicating that additional factors may better explain cognitive decline.

Final Model: Significant Predictors Only

Focus on significant predictors: CDR and nWBV.

\text{MMSE}_{ij} = 17.894 - 5.441 \times \text{CDR}_{ij} + 15.038 \times \text{nWBV}_{ij} + u_{0j} + \epsilon_{ij}

CDR Coefficient: -5.441 (strong negative effect).
nWBV Coefficient: 15.038 (positive effect).

Key Findings

CDR strongly predicts cognitive decline.
Higher nWBV mitigates decline.

Final Model: Significant Predictors Only

R Code

final_model <- lapply(imputed_list, function(data) {
  lmer(MMSE ~ CDR + nWBV + (1 | Subject.ID), data = data)
})
pooled_final_results <- testEstimates(final_model, method = "D2")
summary(pooled_final_results)


Call:

testEstimates(model = final_model, method = "D2")

Final parameter estimates and inferences obtained from 5 imputed data sets.

             Estimate Std.Error   t.value        df   P(>|t|)       RIV       FMI 
(Intercept)    17.621     3.608     4.884 3.284e+06     0.000     0.001     0.001 
CDR            -5.230     0.456   -11.474 1.787e+04     0.000     0.015     0.015 
nWBV           15.349     4.873     3.150 3.891e+06     0.002     0.001     0.001 

Unadjusted hypothesis test as appropriate in larger samples.

Results: CDR was significantly associated with MMSE scores, showing that higher dementia severity leads to lower cognitive function. Additionally, higher nWBV was associated with higher MMSE, supporting its role in cognitive preservation.

Conclusions

Key Takeaways

Age alone does not predict cognitive decline.
Dementia severity (CDR) is a strong negative predictor.
Higher brain volumes (nWBV) are protective against cognitive decline.

References

Agostinelli, C., & Yohai, V. J. (2016). Composite robust estimators for linear mixed models. Journal of the American Statistical Association, 111(516), 1764-1774. https://doi.org/10.1080/01621459.2015.1115358
Bates, D. (2014). Fitting linear mixed-effects models using lme4. arXiv preprint arXiv:1406.5823.
Baayen, R. H., Davidson, D. J., & Bates, D. M. (2008). Mixed-effects modeling with crossed random effects for subjects and items. Journal of Memory and Language, 59(4), 390-412.
Barr, D. J., Levy, R., Scheepers, C., & Tily, H. J. (2013). Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of Memory and Language, 68(3), 255-278.
Bruin, J. (2006). newtest: command to compute new test. UCLA: Statistical Consulting Group. https://stats.oarc.ucla.edu/stata/ado/analysis/.

References (continued)

Enders, C. K. (2010). Applied Missing Data Analysis. Guilford Press.
Gelman, A., & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
Starkweather, J. (2010). Linear mixed effects modeling using R. Unpublished Manuscript.